all_task<- cbind(s2r_abs,s2v_abs) %>%
select(sid, frame_effect_r, frame_effect_v, frame_size)
p_df<- perception_abs %>%
ungroup() %>%
select(magnitude, sid) %>%
rename(sub_1 =sid)
all_task<- cbind(all_task,p_df)
all_task<- all_task %>%
select(-sub_1)
all_task<-all_task %>%
rename(vv= frame_effect_v,
oc = frame_effect_r,
perc = magnitude)
across_frames<- perc_x_sacc_df %>%
pivot_wider(names_from = task, values_from = magnitude)
To determine the change in PSE as a function of frame size, we subtracted the PSE for counterclockwise trials from clockwise trials, and then divided that by half.
We observed a significant effect for each of the frame sizes (all p-values<0.001).
A one-way ANOVA was conducted to evaluate if there was a difference in magnitude between frame sizes, which revealed a main effect of frame size (stats).
A Tukey post hoc analysis revealed a statistically significant difference the small frame and extra large frame, but no other differences were statistically significant.
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 2.11 | 2.00 | 1.15 | -0.27 | 6.35 |
| Medium | 1.91 | 1.71 | 1.12 | 0.15 | 6.68 |
| Large | 1.71 | 1.45 | 1.02 | -0.06 | 4.77 |
| Extra Large | 1.55 | 1.33 | 0.99 | -0.50 | 5.80 |
Perception Task: RFI | |||||||
|---|---|---|---|---|---|---|---|
frame_size | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
175 | 2.11 | 16.44 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.85, 2.37] |
410 | 1.91 | 15.27 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.66, 2.16] |
645 | 1.71 | 14.97 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.48, 1.93] |
880 | 1.55 | 14.03 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.33, 1.77] |
p_mag_anova<- aov(frame_effect_perception ~frame_size, data =perception)
summary(p_mag_anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## frame_size 3 14.3 4.759 4.154 0.0066 **
## Residuals 316 362.0 1.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tukey_p<-tukey_hsd(p_mag_anova)
tukey_p
## # A tibble: 6 × 9
## term group1 group2 null.value estimate conf.low conf.high p.adj p.adj.signif
## * <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 fram… 175 410 0 -0.202 -0.639 0.235 0.631 ns
## 2 fram… 175 645 0 -0.402 -0.839 0.0348 0.0837 ns
## 3 fram… 175 880 0 -0.562 -0.999 -0.125 0.0055 **
## 4 fram… 410 645 0 -0.200 -0.637 0.237 0.638 ns
## 5 fram… 410 880 0 -0.360 -0.797 0.0770 0.146 ns
## 6 fram… 645 880 0 -0.160 -0.597 0.277 0.781 ns
apa_table(tukey_p)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| frame_size | 175 | 410 | 0.00 | -0.20 | -0.64 | 0.24 | 0.63 | ns |
| frame_size | 175 | 645 | 0.00 | -0.40 | -0.84 | 0.03 | 0.08 | ns |
| frame_size | 175 | 880 | 0.00 | -0.56 | -1.00 | -0.12 | 0.01 | ** |
| frame_size | 410 | 645 | 0.00 | -0.20 | -0.64 | 0.24 | 0.64 | ns |
| frame_size | 410 | 880 | 0.00 | -0.36 | -0.80 | 0.08 | 0.15 | ns |
| frame_size | 645 | 880 | 0.00 | -0.16 | -0.60 | 0.28 | 0.78 | ns |
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = frame_effect_perception ~ frame_size, data = perception)
##
## $frame_size
## diff lwr upr p adj
## 410-175 -0.2019557 -0.6390396 0.23512813 0.6314914
## 645-175 -0.4022388 -0.8393226 0.03484511 0.0836585
## 880-175 -0.5620776 -0.9991615 -0.12499376 0.0055008
## 645-410 -0.2002830 -0.6373669 0.23680084 0.6377398
## 880-410 -0.3601219 -0.7972058 0.07696198 0.1464796
## 880-645 -0.1598389 -0.5969227 0.27724500 0.7808421
## $frame_size
## 175 410 645 880
## "a" "ab" "ab" "b"
## # A tibble: 4 × 4
## frame_size mean quant cld_p
## <fct> <dbl> <dbl> <chr>
## 1 175 2.11 2.52 a
## 2 410 1.91 2.18 ab
## 3 645 1.71 2.36 ab
## 4 880 1.55 2.15 b
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame.
We observed a significant effect for each of the frame sizes (all p-values<0.001).
A one-way ANOVA was conducted to evaluate if there was a difference in magnitude between frame sizes, which revealed no main effect of frame size (stats).
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 1.47 | 1.31 | 1.63 | -2.77 | 8.74 |
| Medium | 1.23 | 1.01 | 1.75 | -1.84 | 8.34 |
| Large | 1.14 | 1.04 | 1.35 | -1.63 | 5.91 |
| Extra Large | 1.04 | 0.88 | 1.51 | -2.10 | 8.97 |
s2v_ttest_df<-saccade_to_vert_magnitude %>% group_by(FRAME_SIZE_VAL) %>% do(tidy(t.test(.$frame_effect_v)))
nice_table(s2v_ttest_df)
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | 1.47 | 8.04 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.11, 1.83] |
410 | 1.23 | 6.29 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.62] |
645 | 1.14 | 7.55 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.44] |
880 | 1.04 | 6.16 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.70, 1.37] |
vv_mag_anova<- aov(frame_effect_v~FRAME_SIZE_VAL, data =saccade_to_vert_magnitude)
#summary(vv_mag_anova)
tukey_vv<-tukey_hsd(vv_mag_anova)
apa_table(tukey_vv)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | 175 | 410 | 0.00 | -0.24 | -0.88 | 0.40 | 0.77 | ns |
| FRAME_SIZE_VAL | 175 | 645 | 0.00 | -0.33 | -0.97 | 0.31 | 0.56 | ns |
| FRAME_SIZE_VAL | 175 | 880 | 0.00 | -0.43 | -1.07 | 0.21 | 0.31 | ns |
| FRAME_SIZE_VAL | 410 | 645 | 0.00 | -0.09 | -0.73 | 0.55 | 0.98 | ns |
| FRAME_SIZE_VAL | 410 | 880 | 0.00 | -0.19 | -0.83 | 0.45 | 0.87 | ns |
| FRAME_SIZE_VAL | 645 | 880 | 0.00 | -0.10 | -0.75 | 0.54 | 0.98 | ns |
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = frame_effect_v ~ FRAME_SIZE_VAL, data = saccade_to_vert_magnitude)
##
## $FRAME_SIZE_VAL
## diff lwr upr p adj
## 410-175 -0.23837579 -0.8788647 0.4021131 0.7715415
## 645-175 -0.32587743 -0.9663663 0.3146114 0.5546178
## 880-175 -0.43057760 -1.0710665 0.2099113 0.3066241
## 645-410 -0.08750163 -0.7279905 0.5529872 0.9849084
## 880-410 -0.19220181 -0.8326907 0.4482871 0.8657073
## 880-645 -0.10470017 -0.7451890 0.5357887 0.9746602
## $FRAME_SIZE_VAL
## $FRAME_SIZE_VAL$Letters
## 175 410 645 880
## "a" "a" "a" "a"
##
## $FRAME_SIZE_VAL$LetterMatrix
## a
## 175 TRUE
## 410 TRUE
## 645 TRUE
## 880 TRUE
## `geom_smooth()` using formula = 'y ~ x'
Small Frame
#175
cor_s2v_perc_175
##
## Pearson's product-moment correlation
##
## data: s2v_perc_175$perception and s2v_perc_175$s2v
## t = -0.15077, df = 78, p-value = 0.8805
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2359011 0.2034108
## sample estimates:
## cor
## -0.01706895
Medium Frame
#410
cor_s2v_perc_410
##
## Pearson's product-moment correlation
##
## data: s2v_perc_410$perception and s2v_perc_410$s2v
## t = 4.1293, df = 78, p-value = 9.057e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2247359 0.5884918
## sample estimates:
## cor
## 0.4235391
Large Frame
#645
cor_s2v_perc_645
##
## Pearson's product-moment correlation
##
## data: s2v_perc_645$perception and s2v_perc_645$s2v
## t = 3.7225, df = 78, p-value = 0.0003706
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1844243 0.5603040
## sample estimates:
## cor
## 0.3884026
Extra Large Frame
#880
cor_s2v_perc_880
##
## Pearson's product-moment correlation
##
## data: s2v_perc_880$perception and s2v_perc_880$s2v
## t = 5.6445, df = 78, p-value = 2.569e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3615895 0.6780148
## sample estimates:
## cor
## 0.5385222
Small frame
##
## Call:
## lm(formula = vv ~ perc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1732 -0.9443 -0.1688 0.6118 7.2427
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.52049 0.38651 3.934 0.00018 ***
## perc -0.02429 0.16113 -0.151 0.88055
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.644 on 78 degrees of freedom
## Multiple R-squared: 0.0002913, Adjusted R-squared: -0.01253
## F-statistic: 0.02273 on 1 and 78 DF, p-value: 0.8805
Medium frame
##
## Call:
## lm(formula = vv ~ perc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8382 -0.7158 -0.1747 0.7763 7.6688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.03488 0.35465 -0.098 0.922
## perc 0.66340 0.16066 4.129 9.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.595 on 78 degrees of freedom
## Multiple R-squared: 0.1794, Adjusted R-squared: 0.1689
## F-statistic: 17.05 on 1 and 78 DF, p-value: 9.057e-05
Large frame
##
## Call:
## lm(formula = vv ~ perc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1883 -0.6084 -0.0252 0.6845 4.1134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2630 0.2750 0.956 0.341852
## perc 0.5155 0.1385 3.723 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.256 on 78 degrees of freedom
## Multiple R-squared: 0.1509, Adjusted R-squared: 0.14
## F-statistic: 13.86 on 1 and 78 DF, p-value: 0.0003706
Extra large frame
##
## Call:
## lm(formula = vv ~ perc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7192 -0.7819 -0.0548 0.7057 4.4342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2342 0.2670 -0.877 0.383
## perc 0.8224 0.1457 5.644 2.57e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.278 on 78 degrees of freedom
## Multiple R-squared: 0.29, Adjusted R-squared: 0.2809
## F-statistic: 31.86 on 1 and 78 DF, p-value: 2.569e-07
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame.
We observed a significant effect for each of the frame sizes (all p-values<0.001).
A one-way ANOVA was conducted to evaluate if there was a difference in magnitude between frame sizes, which revealed a main effect of frame size (stats).
A Tukey post hoc analysis revealed a statistically significant differences between the small frame and each of the other frame sizes.
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 1.61 | 1.50 | 1.44 | -4.51 | 6.47 |
| Medium | 0.88 | 0.99 | 1.24 | -2.39 | 4.38 |
| Large | 0.62 | 0.58 | 1.35 | -4.02 | 4.01 |
| Extra Large | 0.76 | 0.70 | 1.14 | -2.57 | 4.76 |
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | 1.61 | 9.98 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.29, 1.93] |
410 | 0.88 | 6.36 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.60, 1.15] |
645 | 0.62 | 4.09 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.32, 0.92] |
880 | 0.76 | 5.94 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.50, 1.01] |
## Df Sum Sq Mean Sq F value Pr(>F)
## FRAME_SIZE_VAL 3 46.9 15.635 9.284 6.7e-06 ***
## Residuals 316 532.2 1.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | Small | Medium | 0.00 | 0.73 | 0.20 | 1.26 | 0.00 | ** |
| FRAME_SIZE_VAL | Small | Large | 0.00 | 0.99 | 0.46 | 1.52 | 0.00 | **** |
| FRAME_SIZE_VAL | Small | Extra Large | 0.00 | 0.85 | 0.32 | 1.38 | 0.00 | *** |
| FRAME_SIZE_VAL | Medium | Large | 0.00 | 0.26 | -0.27 | 0.79 | 0.58 | ns |
| FRAME_SIZE_VAL | Medium | Extra Large | 0.00 | 0.12 | -0.41 | 0.65 | 0.94 | ns |
| FRAME_SIZE_VAL | Large | Extra Large | 0.00 | -0.14 | -0.67 | 0.39 | 0.90 | ns |
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = frame_effect_r ~ FRAME_SIZE_VAL, data = saccade_to_rod_magnitude)
##
## $FRAME_SIZE_VAL
## diff lwr upr p adj
## Medium-Small 0.7300491 0.2000867 1.2600116 0.0024240
## Large-Small 0.9922527 0.4622903 1.5222152 0.0000123
## Extra Large-Small 0.8511250 0.3211626 1.3810875 0.0002514
## Large-Medium 0.2622036 -0.2677589 0.7921661 0.5777345
## Extra Large-Medium 0.1210759 -0.4088866 0.6510384 0.9350444
## Extra Large-Large -0.1411277 -0.6710902 0.3888348 0.9017215
## $FRAME_SIZE_VAL
## Large Extra Large Medium Small
## "a" "a" "a" "b"
## # A tibble: 4 × 4
## FRAME_SIZE_VAL mean quant cld_oc
## <fct> <dbl> <dbl> <chr>
## 1 Large -0.618 0.0408 a
## 2 Extra Large -0.759 -0.151 a
## 3 Medium -0.880 -0.130 a
## 4 Small -1.61 -0.918 b
Small Frame
oc_small<- lm(oc~perc, df_small)
oc_small_summary<- summary(oc_small)
oc_small_summary
##
## Call:
## lm(formula = oc ~ perc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7726 -0.6195 -0.0129 0.6161 4.9510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9789 0.3315 2.953 0.00416 **
## perc 0.2990 0.1382 2.163 0.03357 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.411 on 78 degrees of freedom
## Multiple R-squared: 0.05661, Adjusted R-squared: 0.04451
## F-statistic: 4.68 on 1 and 78 DF, p-value: 0.03357
Medium Frame
##
## Call:
## lm(formula = oc ~ perc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0713 -0.6608 0.0778 0.6634 3.6698
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2801 0.2653 1.056 0.2943
## perc 0.3143 0.1202 2.615 0.0107 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.194 on 78 degrees of freedom
## Multiple R-squared: 0.08061, Adjusted R-squared: 0.06882
## F-statistic: 6.839 on 1 and 78 DF, p-value: 0.0107
Large Frame
##
## Call:
## lm(formula = oc ~ perc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4242 -0.5627 -0.0553 0.7771 2.9618
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2068 0.2767 -0.747 0.457183
## perc 0.4827 0.1393 3.465 0.000866 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.264 on 78 degrees of freedom
## Multiple R-squared: 0.1334, Adjusted R-squared: 0.1223
## F-statistic: 12 on 1 and 78 DF, p-value: 0.0008661
Extra Large Frame
##
## Call:
## lm(formula = oc ~ perc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4423 -0.5788 -0.0889 0.5603 3.4818
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2485 0.2302 1.080 0.2837
## perc 0.3296 0.1256 2.624 0.0105 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.102 on 78 degrees of freedom
## Multiple R-squared: 0.08111, Adjusted R-squared: 0.06933
## F-statistic: 6.885 on 1 and 78 DF, p-value: 0.01045
Small Frame
## # A tibble: 80 × 5
## # Groups: sid, frame_size [80]
## sid oc vv frame_size perc
## <chr> <dbl> <dbl> <fct> <dbl>
## 1 30201cc 2.68 -0.219 175 2.23
## 2 30201ms 2.58 4.78 175 2.09
## 3 30202is 0.463 1.76 175 3.99
## 4 30205gr 1.98 -0.0316 175 -0.273
## 5 30205jp 1.52 0.700 175 0.685
## 6 30205sb -0.468 0.383 175 1.40
## 7 30208lj 4.76 5.06 175 2.38
## 8 30217af 2.10 0.389 175 2.23
## 9 30301av 1.70 0.566 175 2.36
## 10 30301sb 0.822 2.74 175 2.52
## # ℹ 70 more rows
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_small$oc and df_small$vv is
## positive, statistically not significant, and tiny (r = 0.04, 95% CI [-0.19,
## 0.25], t(78) = 0.31, p = 0.756)
## `geom_smooth()` using formula = 'y ~ x'
report(small_vv_oc_cor)
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_small$oc and df_small$vv is
## positive, statistically not significant, and tiny (r = 0.04, 95% CI [-0.19,
## 0.25], t(78) = 0.31, p = 0.756)
Medium Frame
## # A tibble: 80 × 5
## # Groups: sid, frame_size [80]
## sid oc vv frame_size perc
## <chr> <dbl> <dbl> <fct> <dbl>
## 1 30201cc 1.33 -1.19 410 1.72
## 2 30201ms 2.03 4.13 410 3.54
## 3 30202is 1.68 1.34 410 3.17
## 4 30205gr -0.0156 -0.522 410 1.25
## 5 30205jp 0.711 1.56 410 1.70
## 6 30205sb -0.628 0.467 410 0.858
## 7 30208lj 2.31 3.76 410 1.62
## 8 30217af 0.363 -0.368 410 0.991
## 9 30301av 1.62 1.46 410 2.29
## 10 30301sb 0.0478 2.77 410 3.31
## # ℹ 70 more rows
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_medium$oc and df_medium$vv
## is positive, statistically not significant, and very small (r = 0.08, 95% CI
## [-0.14, 0.29], t(78) = 0.70, p = 0.485)
## `geom_smooth()` using formula = 'y ~ x'
report(medium_vv_oc_cor)
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_medium$oc and df_medium$vv
## is positive, statistically not significant, and very small (r = 0.08, 95% CI
## [-0.14, 0.29], t(78) = 0.70, p = 0.485)
Large Frame
## # A tibble: 80 × 5
## # Groups: sid, frame_size [80]
## sid oc vv frame_size perc
## <chr> <dbl> <dbl> <fct> <dbl>
## 1 30201cc 1.26 -0.916 645 1.54
## 2 30201ms 2.97 1.17 645 4.11
## 3 30202is 0.595 2.94 645 3.22
## 4 30205gr 0.669 0.991 645 1.17
## 5 30205jp 0.194 0.445 645 0.985
## 6 30205sb -0.918 1.04 645 0.749
## 7 30208lj 1.86 2.73 645 2.59
## 8 30217af -0.0256 2.11 645 1.03
## 9 30301av 0.656 1.58 645 3.30
## 10 30301sb 1.27 2.87 645 4.03
## # ℹ 70 more rows
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_large$oc and df_large$vv is
## positive, statistically not significant, and small (r = 0.20, 95% CI [-0.02,
## 0.40], t(78) = 1.78, p = 0.078)
## `geom_smooth()` using formula = 'y ~ x'
report(large_vv_oc_cor)
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_large$oc and df_large$vv is
## positive, statistically not significant, and small (r = 0.20, 95% CI [-0.02,
## 0.40], t(78) = 1.78, p = 0.078)
Extra Large Frame
## # A tibble: 80 × 5
## # Groups: sid, frame_size [80]
## sid oc vv frame_size perc
## <chr> <dbl> <dbl> <fct> <dbl>
## 1 30201cc 1.20 -1.34 880 1.47
## 2 30201ms 1.94 1.93 880 2.74
## 3 30202is -0.876 1.89 880 2.58
## 4 30205gr -0.0706 1.62 880 0.747
## 5 30205jp 0.872 0.113 880 0.285
## 6 30205sb 0.298 0.454 880 0.773
## 7 30208lj 0.957 1.91 880 1.30
## 8 30217af -0.750 0.598 880 1.21
## 9 30301av 0.818 1.07 880 2.77
## 10 30301sb -0.645 0.130 880 3.30
## # ℹ 70 more rows
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_medium$oc and df_medium$vv
## is positive, statistically not significant, and very small (r = 0.08, 95% CI
## [-0.14, 0.29], t(78) = 0.70, p = 0.485)
## `geom_smooth()` using formula = 'y ~ x'
report(xl_vv_oc_cor)
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between df_xl$oc and df_xl$vv is
## positive, statistically significant, and medium (r = 0.23, 95% CI [0.02, 0.43],
## t(78) = 2.13, p = 0.037)
Across Frames
## # A tibble: 320 × 5
## # Groups: sid, frame_size [320]
## sid oc vv frame_size perc
## <chr> <dbl> <dbl> <fct> <dbl>
## 1 30201cc 2.68 -0.219 175 2.23
## 2 30201cc 1.33 -1.19 410 1.72
## 3 30201cc 1.26 -0.916 645 1.54
## 4 30201cc 1.20 -1.34 880 1.47
## 5 30201ms 2.58 4.78 175 2.09
## 6 30201ms 2.03 4.13 410 3.54
## 7 30201ms 2.97 1.17 645 4.11
## 8 30201ms 1.94 1.93 880 2.74
## 9 30202is 0.463 1.76 175 3.99
## 10 30202is 1.68 1.34 410 3.17
## # ℹ 310 more rows
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between all_task$oc and all_task$vv is
## positive, statistically significant, and small (r = 0.15, 95% CI [0.04, 0.25],
## t(318) = 2.63, p = 0.009)
## `geom_smooth()` using formula = 'y ~ x'
report(across_vv_oc_cor)
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between all_task$oc and all_task$vv is
## positive, statistically significant, and small (r = 0.15, 95% CI [0.04, 0.25],
## t(318) = 2.63, p = 0.009)
So far the perceptual and orientation contrast effect were reported as negative numbers, indicating that the perceptual response or saccade erred in the opposite direction of the tilt of the frame. However, it should be noted that for the purpose of making an additive comparison between summed saccade tasks and the perceptual response, we used the inverse value of the OC effect.
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_175$perception and comb_sacc_perc_175$combined_saccade
## t = 1.2689, df = 78, p-value = 0.2083
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08000506 0.35096232
## sample estimates:
## cor
## 0.1422117
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_410$perception and comb_sacc_perc_410$combined_saccade
## t = 4.9876, df = 78, p-value = 3.619e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3049679 0.6420802
## sample estimates:
## cor
## 0.4917352
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_645$perception and comb_sacc_perc_645$combined_saccade
## t = 4.9228, df = 78, p-value = 4.662e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2991548 0.6383051
## sample estimates:
## cor
## 0.48687
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_880$perception and comb_sacc_perc_880$combined_saccade
## t = 5.7131, df = 78, p-value = 1.935e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3672545 0.6815287
## sample estimates:
## cor
## 0.543144
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Vertical
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Rod
## `geom_smooth()` using formula = 'y ~ x'
##
## Pearson's product-moment correlation
##
## data: s2r_perc_175$perception and s2r_perc_175$s2r
## t = -2.1634, df = 78, p-value = 0.03357
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.43490358 -0.01920867
## sample estimates:
## cor
## -0.2379214
##
## Pearson's product-moment correlation
##
## data: s2r_perc_410$perception and s2r_perc_410$s2r
## t = -2.6151, df = 78, p-value = 0.0107
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.47405942 -0.06846902
## sample estimates:
## cor
## -0.2839148
##
## Pearson's product-moment correlation
##
## data: s2r_perc_645$perception and s2r_perc_645$s2r
## t = -3.4645, df = 78, p-value = 0.0008661
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5414599 -0.1581624
## sample estimates:
## cor
## -0.3651887
##
## Pearson's product-moment correlation
##
## data: s2r_perc_880$perception and s2r_perc_880$s2r
## t = -2.6239, df = 78, p-value = 0.01045
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.47480242 -0.06942329
## sample estimates:
## cor
## -0.2847961
#two way anova task X frame size summary stats
task_by_frame_long %>%
group_by(frame_size,task) %>%
get_summary_stats(magnitude,type = "mean_sd")
## # A tibble: 8 × 6
## frame_size task variable n mean sd
## <fct> <fct> <fct> <dbl> <dbl> <dbl>
## 1 175 vv magnitude 80 1.47 1.63
## 2 175 oc magnitude 80 1.61 1.44
## 3 410 vv magnitude 80 1.23 1.75
## 4 410 oc magnitude 80 0.88 1.24
## 5 645 vv magnitude 80 1.14 1.35
## 6 645 oc magnitude 80 0.618 1.35
## 7 880 vv magnitude 80 1.04 1.51
## 8 880 oc magnitude 80 0.759 1.14
#box plot
task_frame_bxp<- ggboxplot(
task_by_frame_long, x = "frame_size", y = "magnitude", color = "task", pallet ="jco")
task_frame_bxp
For each frame size a hierarchical design was employed using two models: 1) model 1 predicted the overall RFI magnitude (measured by the perception task) from the visuovestibular effect (measured by the saccade-to-vertical task) and 2) model 2 predicted the overall RFI magnitude from visuovestibular effect and the orientation contrast effect (measured by the saccade-to-rod task).
Perceptual effect predicted by visuovestibular effect
##
## Call:
## lm(formula = vv ~ perc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1732 -0.9443 -0.1688 0.6118 7.2427
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.52049 0.38651 3.934 0.00018 ***
## perc -0.02429 0.16113 -0.151 0.88055
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.644 on 78 degrees of freedom
## Multiple R-squared: 0.0002913, Adjusted R-squared: -0.01253
## F-statistic: 0.02273 on 1 and 78 DF, p-value: 0.8805
Perceptual effect predicted by orientation contrast effect
##
## Call:
## lm(formula = oc ~ perc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7726 -0.6195 -0.0129 0.6161 4.9510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9789 0.3315 2.953 0.00416 **
## perc 0.2990 0.1382 2.163 0.03357 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.411 on 78 degrees of freedom
## Multiple R-squared: 0.05661, Adjusted R-squared: 0.04451
## F-statistic: 4.68 on 1 and 78 DF, p-value: 0.03357
Model comparison
Model 1: perceptual effect~visuovestibular Model 2: perceptual ~ visuovestibular+ orientation contrast
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4789 -0.6643 -0.1876 0.3187 4.2826
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.83034 0.21902 8.357 2.08e-12 ***
## vv -0.01792 0.07779 -0.230 0.8184
## oc 0.19003 0.08810 2.157 0.0341 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.129 on 77 degrees of freedom
## Multiple R-squared: 0.05726, Adjusted R-squared: 0.03277
## F-statistic: 2.338 on 2 and 77 DF, p-value: 0.1033
## [1] 0.05696534
## Warning in anova.lmlist(object, ...): models with response '"perc"' removed
## because response differs from model 1
## Analysis of Variance Table
##
## Response: vv
## Df Sum Sq Mean Sq F value Pr(>F)
## perc 1 0.061 0.06147 0.0227 0.8805
## Residuals 78 210.933 2.70427
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.520 | 1.830 |
| (0.387) | (0.219) | |
| perc | -0.024 | |
| (0.161) | ||
| vv | -0.018 | |
| (0.078) | ||
| oc | 0.190 | |
| (0.088) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.000 | 0.057 |
| R2 Adj. | -0.013 | 0.033 |
| AIC | 310.6 | 251.4 |
| BIC | 317.7 | 260.9 |
| Log.Lik. | -152.296 | -121.710 |
| RMSE | 1.62 | 1.11 |
Perceptual effect predicted by visuovestibular effect
summary(model_1_medium)
##
## Call:
## lm(formula = vv ~ perc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8382 -0.7158 -0.1747 0.7763 7.6688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.03488 0.35465 -0.098 0.922
## perc 0.66340 0.16066 4.129 9.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.595 on 78 degrees of freedom
## Multiple R-squared: 0.1794, Adjusted R-squared: 0.1689
## F-statistic: 17.05 on 1 and 78 DF, p-value: 9.057e-05
Perceptual effect predicted by orientation contrast effect
##
## Call:
## lm(formula = oc ~ perc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0713 -0.6608 0.0778 0.6634 3.6698
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2801 0.2653 1.056 0.2943
## perc 0.3143 0.1202 2.615 0.0107 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.194 on 78 degrees of freedom
## Multiple R-squared: 0.08061, Adjusted R-squared: 0.06882
## F-statistic: 6.839 on 1 and 78 DF, p-value: 0.0107
Model comparison
Model 1: perceptual effect~visuovestibular Model 2: perceptual ~ visuovestibular+ orientation contrast
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.92902 -0.56106 -0.08099 0.47815 3.13629
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.39053 0.15335 9.068 8.87e-14 ***
## vv 0.25768 0.06352 4.056 0.000118 ***
## oc 0.22763 0.08988 2.533 0.013356 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.985 on 77 degrees of freedom
## Multiple R-squared: 0.2425, Adjusted R-squared: 0.2228
## F-statistic: 12.32 on 2 and 77 DF, p-value: 2.273e-05
## [1] 0.0631005
## Warning in anova.lmlist(object, ...): models with response '"perc"' removed
## because response differs from model 1
## Analysis of Variance Table
##
## Response: vv
## Df Sum Sq Mean Sq F value Pr(>F)
## perc 1 43.40 43.400 17.051 9.057e-05 ***
## Residuals 78 198.54 2.545
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | -0.035 | 1.391 |
| (0.355) | (0.153) | |
| perc | 0.663 | |
| (0.161) | ||
| vv | 0.258 | |
| (0.064) | ||
| oc | 0.228 | |
| (0.090) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.179 | 0.242 |
| R2 Adj. | 0.169 | 0.223 |
| AIC | 305.7 | 229.5 |
| BIC | 312.9 | 239.1 |
| Log.Lik. | -149.873 | -110.775 |
| RMSE | 1.58 | 0.97 |
Perceptual effect predicted by visuovestibular effect
##
## Call:
## lm(formula = vv ~ perc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1883 -0.6084 -0.0252 0.6845 4.1134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2630 0.2750 0.956 0.341852
## perc 0.5155 0.1385 3.723 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.256 on 78 degrees of freedom
## Multiple R-squared: 0.1509, Adjusted R-squared: 0.14
## F-statistic: 13.86 on 1 and 78 DF, p-value: 0.0003706
Perceptual effect predicted by orientation contrast effect
##
## Call:
## lm(formula = oc ~ perc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4242 -0.5627 -0.0553 0.7771 2.9618
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2068 0.2767 -0.747 0.457183
## perc 0.4827 0.1393 3.465 0.000866 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.264 on 78 degrees of freedom
## Multiple R-squared: 0.1334, Adjusted R-squared: 0.1223
## F-statistic: 12 on 1 and 78 DF, p-value: 0.0008661
Model comparison
Model 1: perceptual effect~visuovestibular Model 2: perceptual ~ visuovestibular+ orientation contrast
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6401 -0.5876 -0.2332 0.2946 3.9705
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.28410 0.13581 9.455 1.59e-14 ***
## vv 0.24787 0.07650 3.240 0.00177 **
## oc 0.22699 0.07681 2.955 0.00415 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9027 on 77 degrees of freedom
## Multiple R-squared: 0.2373, Adjusted R-squared: 0.2175
## F-statistic: 11.98 on 2 and 77 DF, p-value: 2.948e-05
## [1] 0.08649254
## Warning in anova.lmlist(object, ...): models with response '"perc"' removed
## because response differs from model 1
## Analysis of Variance Table
##
## Response: vv
## Df Sum Sq Mean Sq F value Pr(>F)
## perc 1 21.864 21.8644 13.857 0.0003706 ***
## Residuals 78 123.070 1.5778
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 0.263 | 1.284 |
| (0.275) | (0.136) | |
| perc | 0.516 | |
| (0.138) | ||
| vv | 0.248 | |
| (0.076) | ||
| oc | 0.227 | |
| (0.077) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.151 | 0.237 |
| R2 Adj. | 0.140 | 0.218 |
| AIC | 267.5 | 215.6 |
| BIC | 274.6 | 225.1 |
| Log.Lik. | -130.744 | -103.798 |
| RMSE | 1.24 | 0.89 |
Perceptual effect predicted by visuovestibular effect
##
## Call:
## lm(formula = vv ~ perc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7192 -0.7819 -0.0548 0.7057 4.4342
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2342 0.2670 -0.877 0.383
## perc 0.8224 0.1457 5.644 2.57e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.278 on 78 degrees of freedom
## Multiple R-squared: 0.29, Adjusted R-squared: 0.2809
## F-statistic: 31.86 on 1 and 78 DF, p-value: 2.569e-07
Perceptual effect predicted by orientation contrast effect
##
## Call:
## lm(formula = oc ~ perc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4423 -0.5788 -0.0889 0.5603 3.4818
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2485 0.2302 1.080 0.2837
## perc 0.3296 0.1256 2.624 0.0105 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.102 on 78 degrees of freedom
## Multiple R-squared: 0.08111, Adjusted R-squared: 0.06933
## F-statistic: 6.885 on 1 and 78 DF, p-value: 0.01045
Model comparison
Model 1: perceptual effect~visuovestibular Model 2: perceptual ~ visuovestibular+ orientation contrast
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73611 -0.57671 0.00541 0.53652 2.24999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.09815 0.12229 8.980 1.31e-13 ***
## vv 0.32691 0.06345 5.152 1.93e-06 ***
## oc 0.14516 0.08372 1.734 0.0869 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8264 on 77 degrees of freedom
## Multiple R-squared: 0.3167, Adjusted R-squared: 0.2989
## F-statistic: 17.84 on 2 and 77 DF, p-value: 4.294e-07
## [1] 0.02668074
## Warning in anova.lmlist(object, ...): models with response '"perc"' removed
## because response differs from model 1
## Analysis of Variance Table
##
## Response: vv
## Df Sum Sq Mean Sq F value Pr(>F)
## perc 1 52.044 52.044 31.86 2.569e-07 ***
## Residuals 78 127.415 1.634
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | -0.234 | 1.098 |
| (0.267) | (0.122) | |
| perc | 0.822 | |
| (0.146) | ||
| vv | 0.327 | |
| (0.063) | ||
| oc | 0.145 | |
| (0.084) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.290 | 0.317 |
| R2 Adj. | 0.281 | 0.299 |
| AIC | 270.3 | 201.5 |
| BIC | 277.4 | 211.0 |
| Log.Lik. | -132.132 | -96.732 |
| RMSE | 1.26 | 0.81 |